Legged locomotion is not just about mobility; it also encompasses crucial objectives such as energy efficiency, safety, and user experience, which are vital for real-world applications. However, key factors such as battery power consumption and stepping noise are often inaccurately modeled or missing in common simulators, leaving these aspects poorly optimized or unaddressed by current sim-to-real methods. Hand-designed proxies, such as mechanical power and foot contact forces, have been used to address these challenges but are often problem-specific and inaccurate. In this paper, we propose a data-driven framework for fine-tuning locomotion policies, targeting these hard-to-simulate objectives. Our framework leverages real-world data to model these objectives and incorporates the learned model into simulation for policy improvement. We demonstrate the effectiveness of our framework on power saving for quadruped locomotion, achieving a significant 24-28\% net reduction in total power consumption from the battery pack at various speeds. In essence, our approach offers a versatile solution for optimizing hard-to-simulate objectives in quadruped locomotion, providing an easy-to-adapt paradigm for continual improving with real-world knowledge. Project page https://hard-to-sim.github.io/.

Robust locomotion control depends on accurate state estimations. However, the sensors of most legged robots can only provide partial and noisy observations, making the estimation particularly challenging, especially for external states like terrain frictions and elevation maps. Inspired by the classical Internal Model Control principle, we consider these external states as disturbances and introduce Hybrid Internal Model (HIM) to estimate them according to the response of the robot. The response, which we refer to as the hybrid internal embedding, contains the robot's explicit velocity and implicit stability representation, corresponding to two primary goals for locomotion tasks: explicitly tracking velocity and implicitly maintaining stability. We use contrastive learning to optimize the embedding to be close to the robot's successor state, in which the response is naturally embedded. HIM has several appealing benefits: It only needs the robot's proprioceptions, i.e., those from joint encoders and IMU as observations. It innovatively maintains consistent observations between simulation reference and reality that avoids information loss in mimicking learning. It exploits batch-level information that is more robust to noises and keeps better sample efficiency. It only requires 1 hour of training on an RTX 4090 to enable a quadruped robot to traverse any terrain under any disturbances. A wealth of real-world experiments demonstrates its agility, even in high-difficulty tasks and cases never occurred during the training process, revealing remarkable open-world generalizability.

Understanding and characterizing the vulnerability of urban infrastructures, which refers to the engineering facilities essential for the regular running of cities and that exist naturally in the form of networks, is of great value to us. Potential applications include protecting fragile facilities and designing robust topologies, etc. Due to the strong correlation between different topological characteristics and infrastructure vulnerability and their complicated evolution mechanisms, some heuristic and machine-assisted analysis fall short in addressing such a scenario. In this paper, we model the interdependent network as a heterogeneous graph and propose a system based on graph neural network with reinforcement learning, which can be trained on real-world data, to characterize the vulnerability of the city system accurately. The presented system leverages deep learning techniques to understand and analyze the heterogeneous graph, which enables us to capture the risk of cascade failure and discover vulnerable infrastructures of cities. Extensive experiments with various requests demonstrate not only the expressive power of our system but also transferring ability and necessity of the specific components.